If \(V\in {\cal L}_{m,n}(q,Q)\) , then \(V\)  is a \((m+n-1)\times (m+n-1)\)  diagonally dominant, symmetric
nonnegative matrix. Define \(v_{m+n,i}=v_{i,m+n}:=v_{i,i}-\sum _{j=1}^{m+n-1}v_{i,j}\)  for \(i=1,\dots ,m+n-1\)  and \(v_{m+n,m+n}=\sum _{i=1}^{m+n-1}v_{m+n,i}.\)  Then \(q\le v_{m+n,i}\le Q\)  for \(i=1,\dots ,m,v_{m+n,i}=0\)  for \(i=m,m+1,\dots ,m+n-1\)  and \(v_{m+n,m+n}=\sum _{i=1}^{m}v_{i,m+n}=\sum _{i=1}^{m}v_{m+n,i}.\) 
The Fisher information matrix of the parameter vector \(\theta \) , \(V\) ,
belongs to the matrix class \(V\in {\cal L}_{m,n}(q,Q)\) .
The approximate error using \(S\)  in (REF ) to approximate the inverse of \(V\) 
is given in the lemma below, whose proof is the extension of that for Proposition 1 in [1]}.
